In this test, the temperature exceeds several \(10^3\)  K, above which all grains should be quickly destroyed by evaporation or sputtering [1]}. This is, however, not an issue since at such high temperatures, the contribution of the (computed) charge of grains is negligible compared to that from ions and electrons. It is also possible to combine our method with any grain destruction model. [2]} assumed that the grain evaporation would occur between \(\sim 800\)  K and \(\sim 1600\)  K in the density range \(n_\mathrm {H}\approx 10^{16} - 10^{19}\)  cm\(^{-3}\) , which coincides with the beginning of the thermal ionization of K and Na.
The species \(s\)  is assumed to be K, Na, or H, using the values of Table REF . [3]} show that K and Na may originally be confined to grains and have to be evaporated before being available for thermal ionization. Our method is compatible with models accounting for that process since \(n_{\mathrm {s},0}\)  can be freely modified at any time. For simplicity, however, we assume here that K and Na are already present in the gas phase in quantities given by \(n_{\mathrm {s},0}\)  in the table.
Here, we present the evolution of \(n_\mathrm {i}/n_\mathrm {H}\) , \(n_\mathrm {s}/n_\mathrm {H}\) , \(n_\mathrm {e}/n_\mathrm {H}\)  and the average grain charge for several bins. The results are displayed in Figures REF , REF , and REF , respectively.
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